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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #16 : Coordinate Geometry

Find the midpoint of a line segment that has endpoints at (-9,-1) and (1,2).

Possible Answers:

$(-\frac{7}{2}, -\frac{1}{2})$

$(-\frac{11}{2}, 0)$

$(-\frac{1}{2}, -\frac{5}{2})$

$(-4, \frac{1}{2})$

Correct answer:

$(-4, \frac{1}{2})$

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{-9+1}{2}, \frac{-1+2}{2})=(-4, \frac{1}{2})$

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Example Question #17 : Coordinate Geometry

Find the midpoint of a line segment with endpoints at (10, 2) and (-2, -8).

Possible Answers:

(4, -3)

(3, 4)

(-9, 2)

(1, 2)

Correct answer:

(4, -3)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{10-2}{2}, \frac{2-8}{2})=(4, -3)$

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Example Question #18 : Coordinate Geometry

Find the midpoint of a line segment that has endpoints at (5,1) and (-3, -10).

Possible Answers:

$(4, \frac{9}{2})$

$(-\frac{5}{2}, -1)$

$(1, -\frac{9}{2})$

$(-\frac{11}{2}, 2)$

Correct answer:

$(1, -\frac{9}{2})$

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{5-3}{2}, \frac{1-10}{2})=(1, -\frac{9}{2})$

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Example Question #19 : Coordinate Geometry

Find the midpoint of a line segment that has endpoints at (0.6, 9) and (-9.2, 7).

Possible Answers:

(-4.8, -2)

(-4.2, 0)

(-4.3, 8)

(-4.9, 1)

Correct answer:

(-4.3, 8)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{0.6-9.2}{2}, \frac{9+7}{2})=(-4.3, 8)$

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Example Question #20 : Coordinate Geometry

Find the midpoint of a line segment that has endpoints at (12, 12) and (-10, 24).

Possible Answers:

(2, 12)

(13, 4)

(11, 13)

(1, 18)

Correct answer:

(1, 18)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{12-10}{2}, \frac{12+24}{2})=(1,18)$

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Example Question #21 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at $\left(\frac{1}{2}, 5\right)$ and $\left(-\frac{3}{2}, 1\right)$ .

Possible Answers:

$(-\frac{3}{4}, 6)$

$(-\frac{1}{2}, -\frac{1}{2})$

$(-\frac{1}{2}, 2)$

$(-\frac{1}{2}, 3)$

Correct answer:

$(-\frac{1}{2}, 3)$

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{\frac{1}{2}-\frac{3}{2}}{2}, \frac{5+1}{2})=(-\frac{1}{2}, 3)$

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Example Question #22 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (9, 120) and (-24, 2) .

Possible Answers:

$(\frac{15}{2}, 61)$

$(-\frac{15}{2}, 61)$

$(-\frac{15}{2}, 59)$

$(-\frac{33}{2}, 60)$

Correct answer:

$(-\frac{15}{2}, 61)$

Explanation:

Recall how to find the midpoint of a line segment with endpoints at (x_1, y_1) and (x_2, y_2) :

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

$\text{Midpoint}=(\frac{9+(-24)}{2}, \frac{120+2}{2})=(-\frac{15}{2}, 61)$

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Example Question #23 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (16, 7) and (8, 9) .

Possible Answers:

(12, 8)

(1, 8)

$(\frac{25}{2}, \frac{15}{2})$

(4, -1)

Correct answer:

(12, 8)

Explanation:

Recall how to find the midpoint of a line segment with endpoints at (x_1, y_1) and (x_2, y_2) :

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

$\text{Midpoint}=(\frac{16+8}{2}, \frac{7+9}{2})=(12, 8)$

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Example Question #24 : Midpoint Formula

A line segment on the coordinate plane has its endpoints at (3.8, -1.7) and (9.2, 5.5) .

True or false: Its midpoint is located at (6.5, 3.6) .

Possible Answers:

True

False

Correct answer:

False

Explanation:

The midpoint of a line segment with endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is located at $\left ( \frac{x_{1}+x_{2}}{2} , \frac{y_{1}+ y_{2}}{2} \right )$ .

Set $x_{1}= 3.8, y_{1} =-1.7,x_{2} =9.2, y_{2}= 5.5$ , and evaluate both expressions:

$\frac{x_{1}+x_{2}}{2}= \frac{3.8+9.2}{2} = \frac{13}{2} = 6.5$

$\frac{-1.7+5.5}{2} =\frac{3.8}{2} = 1.9$

The midpoint is at (6.5, 1.9) , so the statement is false.

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Example Question #1 : How To Find The Endpoints Of A Line Segment

Find the midpoint between the points:

(0,4) and (2,8)

Possible Answers:

(1,6)

(1,7)

(0,0)

(1,1)

(2,4)

Correct answer:

(1,6)

Explanation:

The midpoint formula is

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

So for our two points the equation is

$\left(\frac{0+2}{2},\frac{4+8}{2}\right)$

$\left(\frac{2}{2},\frac{12}{2}\right)$

(1,6)

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #16 : Coordinate Geometry

Example Question #17 : Coordinate Geometry

Example Question #18 : Coordinate Geometry

Example Question #19 : Coordinate Geometry

Example Question #20 : Coordinate Geometry

Example Question #21 : Midpoint Formula

Example Question #22 : Midpoint Formula

Example Question #23 : Midpoint Formula

Example Question #24 : Midpoint Formula

Example Question #1 : How To Find The Endpoints Of A Line Segment

All Intermediate Geometry Resources

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